Solve (3/2x^3+4/3)*(4/2x^2+2/4)

$$( \frac { 3 } { 2 } x ^ { 3 } + \frac { 4 } { 3 } ) \cdot ( \frac { 4 } { 2 } x ^ { 2 } + \frac { 2 } { 4 } )$$

Evaluate

$$\frac{\left(4x^{2}+1\right)\left(9x^{3}+8\right)}{12}$$

Solution Steps

Divide 4 by 2 to get 2.

$$\left(\frac{3}{2}x^{3}+\frac{4}{3}\right)\left(2x^{2}+\frac{2}{4}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{3}{2}x^{3}+\frac{4}{3}\right)\left(2x^{2}+\frac{1}{2}\right)$$

Use the distributive property to multiply \frac{3}{2}x^{3}+\frac{4}{3} by 2x^{2}+\frac{1}{2}.

$$3x^{5}+\frac{3}{4}x^{3}+\frac{8}{3}x^{2}+\frac{2}{3}$$

Expand

$$3x^{5}+\frac{3x^{3}}{4}+\frac{8x^{2}}{3}+\frac{2}{3}$$

Solution Steps

Divide 4 by 2 to get 2.

$$\left(\frac{3}{2}x^{3}+\frac{4}{3}\right)\left(2x^{2}+\frac{2}{4}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{3}{2}x^{3}+\frac{4}{3}\right)\left(2x^{2}+\frac{1}{2}\right)$$

Use the distributive property to multiply \frac{3}{2}x^{3}+\frac{4}{3} by 2x^{2}+\frac{1}{2}.

$$3x^{5}+\frac{3}{4}x^{3}+\frac{8}{3}x^{2}+\frac{2}{3}$$